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The Acropolis of Athens (468–430 BC), including the Parthenon, according to some studies, has many proportions that approximate the golden ratio. [10] Other scholars question whether the golden ratio was known to or used by Greek artists and architects as a principle of aesthetic proportion. [ 11 ]
Some studies of the Acropolis, including of the Parthenon and its facade, have conjectured that many of its proportions approximate the golden ratio. [74] More recent studies have shown that the proportions of the Parthenon do not match the golden proportion. [75] [76]
The golden ratio φ and its negative reciprocal −φ −1 are the two roots of the quadratic polynomial x 2 − x − 1. The golden ratio's negative −φ and reciprocal φ −1 are the two roots of the quadratic polynomial x 2 + x − 1. The golden ratio is also an algebraic number and even an algebraic integer.
Phidias Showing the Frieze of the Parthenon to his Friends (1868) by Sir Lawrence Alma-Tadema. Phidias or Pheidias (/ ˈ f ɪ d i ə s /; Ancient Greek: Φειδίας, Pheidias; c. 480 – c. 430 BC) was an Ancient Greek sculptor, painter, and architect, active in the 5th century BC.
The math involved a more complex geometrical progression, the so-called golden mean. The ratio is similar to that of the growth patterns of many spiral forms that occur in nature such as rams' horns, nautilus shells, fern fronds, and vine tendrils and which were a source of decorative motifs employed by ancient Greek architects as particularly ...
Mnesikles had planned a gatehouse composed of five halls: a central hall that would be the processional route to the Acropolis, two perpendicular flanking halls – north and south of the central hall – that would have spanned the whole width of the western end of the plateau, and two further, eastward projecting halls that were at 90 degrees ...
The addition may have been made so that the width:length ratio of the temple would be closer to the golden ratio, which became popular in temple construction at this time. [41] The remains of the roof consist of 88 fragments from marble tiles (30 cover tiles, 58 pan tiles, 1 end ridge tile) and 4 marble antefixes.
The reconstructed Pergamon Altar in the Pergamon Museum in Berlin. Side view Carl Humann's 1881 plan of the Pergamon acropolis. The Pergamon Altar (Ancient Greek: Βωμός τῆς Περγάμου) was a monumental construction built during the reign of the Ancient Greek King Eumenes II in the first half of the 2nd century BC on one of the terraces of the acropolis of Pergamon in Asia Minor ...